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arxiv: 1110.1053 · v5 · pith:R7Q6GS7Dnew · submitted 2011-10-05 · 🧮 math.CA

Computing the Galois group of some parameterized linear differential equation of order two

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keywords differentialequationgaloisgivegrouplinearorderparameterized
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We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition for the integrability of the system. We give various examples of computation.

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